Solve for $x$ and $y$ using elimination. ${2x-2y = -2}$ ${-5x+2y = -16}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-2y$ and $2y$ cancel out. $-3x = -18$ $\dfrac{-3x}{{-3}} = \dfrac{-18}{{-3}}$ ${x = 6}$ Now that you know ${x = 6}$ , plug it back into $\thinspace {2x-2y = -2}\thinspace$ to find $y$ ${2}{(6)}{ - 2y = -2}$ $12-2y = -2$ $12{-12} - 2y = -2{-12}$ $-2y = -14$ $\dfrac{-2y}{{-2}} = \dfrac{-14}{{-2}}$ ${y = 7}$ You can also plug ${x = 6}$ into $\thinspace {-5x+2y = -16}\thinspace$ and get the same answer for $y$ : ${-5}{(6)}{ + 2y = -16}$ ${y = 7}$